Structural effects and hydrogen bonds on N,N `-di(methoxycarbonylsulfenyl)urea, [CH(3)OC(O)SNH](2)CO, studied by experimental and theoretical methods

Pure N,N`-di(methoxycarbonylsulfenyl)urea, [CH(3)OC(O)SNH](2)CO, is quantitatively prepared by the hydrolysis reaction of CH(3)OC(O)SNCO and characterized by (1)H NMR, GC-MS and FTIR spectroscopy techniques. Structural and conformational properties are analyzed using a combined approach with data obtained from X-ray diffraction, vibrational spectra and theoretical calculation methods. The IR and Raman spectra for normal and deuterated species are reported. The crystal structure of [CH(3)OC(O)SNH](2)CO was determined by X-ray diffraction methods. The substance crystallizes in the orthorhombic P2(1)2(1)2 space group with a = 9.524(2), b = 12.003(1), c = 4.481 (1) angstrom, and Z = 2 moieties in the unit cell. The molecule is sited on a twofold crystallographic axis (C(2)) parallel to c and shows the anti-anti conformation (S-N single bonds antiperiplanar with respect to the opposite C-N single bonds in sulfenyl-urea-sic group). Neighboring molecules are arranged in a chain motif that extends along the C(2)-axis and is held by bifurcated NH center dot center dot center dot O center dot center dot center dot HN intermolecular bonds. A local planar symmetry is observed in the crystal for the central -SN(H)C(O)N(H)S- skeleton. Experimental and calculated data allow to trace this structural feature to the occurrence of N-H center dot center dot center dot O=C hydrogen bonding interactions. Calculated vibrational and structural properties are in good agreement with the experimentally determined features. (C) 2008 Elsevier B.V. All rights reserved.

On the relationships between molecular conformations and intermolecular contacts toward crystal self-assembly of mono-, di-, tri-, and tetra-oxygenated xanthone derivatives

Oxygenated xanthones have been extensively investigated over the years, but there are few reports concerning their crystal structure. Our chemical investigations of Brazilian plants resulted in the isolation of four natural products named 1-hydroxyxanthone (I), 1-hydroxy-7-methoxyxanthone (II), 1,5-dihydroxy-3-methoxyxanthone (III), and 1,7-dihydroxy-3,8-dimethoxyxanthone (IV). The structures of these compounds were established on the basis of single crystal X-ray diffraction. The xanthone nucleus conformation is essentially planar with the substituents adopting the orientations less sterically hindered. In addition, classical intermolecular hydrogen bonds (O-H center dot center dot center dot O) present in III and IV give rise to infinite ribbons. However, the xanthone I does not present any intermolecular hydrogen bonds, meanwhile the xanthone II presents only a non-classical one (C-H center dot center dot center dot O). The crystal packing of all xanthone structures is also stabilized by pi-pi interactions. The fingerprint plots, derived from the Hirshfeld surfaces, exhibited significant features of each crystal structures.

Lie properties of symmetric elements in group rings

Let * be an involution of a group G extended linearly to the group algebra KG. We prove that if G contains no 2-elements and K is a field of characteristic p, 0 2, then the *-symmetric elements of KG are Lie nilpotent (Lie n-Engel) if and only if KG is Lie nilpotent (Lie n-Engel). (C) 2008 Elsevier Inc. All rights reserved.

Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

Lie properties of crossed products

Let F-sigma(lambda)vertical bar G vertical bar be a crossed product of a group G and the field F. We study the Lie properties of F-sigma(lambda)vertical bar G vertical bar in order to obtain a characterization of those crossed products which are upper (lower) Lie nilpotent and Lie (n, m)-Engel. (C) 2008 Elsevier Inc. All rights reserved.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

On E-functions of semisimple Lie groups

We develop and describe continuous and discrete transforms of class functions on a compact semisimple, but not simple, Lie group G as their expansions into series of special functions that are invariant under the action of the even subgroup of the Weyl group of G. We distinguish two cases of even Weyl groups-one is the direct product of even Weyl groups of simple components of G and the second is the full even Weyl group of G. The problem is rather simple in two dimensions. It is much richer in dimensions greater than two-we describe in detail E-transforms of semisimple Lie groups of rank 3.

Some examples of nil Lie algebras

Generalizing Petrogradsky`s construction, we give examples of infinite-dimensional nil Lie algebras of finite Gelfand-Kirillov dimension over any field of positive characteristic.

ON SPECIALITY OF BINARY-LIE ALGEBRAS

In the present work, binary-Lie, assocyclic, and binary (-1,1) algebras are studied. We prove that, for every assocyclic algebra A, the algebra A(-) is binary-Lie. We find a simple non-Malcev binary-Lie superalgebra T that cannot be embedded in A(-s) for an assocyclic superalgebra A. We use the Grassmann envelope of T to prove the similar result for algebras. This solve negatively a problem by Filippov (see [1, Problem 2.108]). Finally, we prove that the superalgebra T is isomorphic to the commutator superalgebra A(-s) for a simple binary (-1,1) superalgebra A.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

Adsorption of di-2-pyridyl ketone salicyloylhydrazone on Amberlite XAD-2 and XAD-7 resins: Characteristics and isotherms

The adsorption of DPKSH onto Amberlite XAD-2 (styrene resin) and XAD-7 (acrylic ester resin) has been investigated, at (25 +/- 1)degrees C and pH 4.7. The experimental equilibrium data were fitted to the Langmuir, Freundlich, and Dubinin-Radushkevich (D-R) models. These three models provide a very good fit for both resins and the respective constants K(L), K(F), and K(DR) were calculated. For the same DPKSH concentration interval, the minimum time of contact for adsorption maximum at XAD-7 was smaller than at XAD-2 and the maximum amount of DPKSH adsorbed per gram of XAD-2 is smaller than at XAD-7. The investigation indicates that the mean sorption energy (E) characterizes a physical adsorption and the surfaces of both resins are energetically heterogeneous. The constants obtained in these studied systems were correlated and compared with those obtained for the silica gel/DPKSH system. (C) 2008 Published by Elsevier Inc.

Spectrophotometric determination of zinc in pharmaceutical and biological samples with di-2-pyridyl ketone benzoylhydrazone: A simple, fast, accurate and sensitive method

A simple, fast, accurate, and sensitive spectrophotometric method was developed to determine zinc(II). This method is based on the reaction of Zn(II) with di-2-pyridyl ketone benzoylhydrazone (DPKBH), at pH=5.5 and 50% (v/v) ethanol. Beers law was obeyed in the range 0.020-1.82 mu g mL(-1) with a molar apsorptivity of 3.64 x 10(4) L mol(-1) cm(-1), and a detection limit (3) of 2.29 mu g L-1. The action of some interfering ions was verified and the developed method applied to pharmaceutical and biological samples. The results were then compared with those obtained by using a flame atomic absorption technique.